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### Regular polygonal plate Stress and Deflection Equation and Calculator

Regular polygonal plate; all edges simply supported with uniform loading over entire plate Stress and Deflection Equation and Calculator.

Per. Roarks Formulas for Stress and Strain for flat plates with straight boundaries and constant thickness

 Regular Polygonal Plate Uniform Loading over entire plate Stress at center Deflection Maximum slope at center of straight edge n 3 4 5 6 7 8 9 10 15 ∞ β 1.302 1.152 1.086 1.056 1.044 1.038 1.038 1.044 1.074 1.236 α 0.91 0.71 0.635 0.599 0.581 0.573 0.572 0.572 0.586 0.695 ε 1.535 1.176 1.028 0.951 0.91 0.888 0.877 0.871 0.883 1.050

Where:

q = Applied load (force) (lbs/in2)
v = Poisson’s ratio (assumed to be 0.3)
E = Modulus of Elasticity (lb/in2)
a = Radius of tangent circle (in)
t = Plate thickness (in)
σ = stress, (lbs/in2)
n = number of sides
β = Constant from table
α = Constant from table
ε = Constant from table

Reference:

Roarks Formulas for Stress and Strain, 7th Edition 